(chapter 6) Example:

A gas stream consisting of n-hexane in methane is fed to a condenser at 60°C and 1.2 atm. The dew point of the gas (considering hexane as the only condensable component) is 55°C. The gas is cooled to 5°C in the condenser, recovering pure hexane as a liquid. The effluent gas leaves the condenser saturate with hexane at 5°C and 1.1 atm and is fed to a noiler furnace at a rate of 207.4 L/s.

a) Calculate the mole fracions of hexane in the condenser feed and product gas streanms and the rate of hexane condensation.

Initial sketch:

Flow diagram:

Our Table has the form:


Totaln-HexaneMethane
F1
F2
F3
X

With all flow rates in mol/s


Now, we fill in the table.
The ideal gas law in stream two, with 1.1 atm, 207 L/s, and 278.25 K gives F2 total.

Totaln-HexaneMethane
F1
F29.992
F3
X


Now, additionally, if we consider Raoult's Law for stream 2, a vapor mixture, which is in equilibrium with stream 3, pure n-Hexane liquid. Raoult's Law is, again:

y2H * P = x3H * PH*


x3H = 1,
P = 1.1 atm
PH* = something we know, we are given the temperature, so we can calculate this with Antoines Equation, and from the appendix B4, we have. PH* = 10^(a - b/(c + T(in °C)), with a = 6.88555, b = 1175.817, c = 224.867, and T = 5, this gives and answer in mmHg (58.93). Thus now have y2H from Raoults law (.07049), and also, since y2M = 1 - y2H, we have y2H = .9295, and thus,

Totaln-HexaneMethane
F1
F29.992.70449.287
F3
X


and, furthermore,

Totaln-HexaneMethane
F19.287
F29.992.70449.287
F3
X


Now, we can apply Raoult's Law to the inlet stream. This seems weird, cause there is only vapor and it is not at it's dew point, but because we know the dew point of the vapor and because there is only one condensible species, we can recall

yH1 * P = PH2*(Tdp)


Now, as before, we have P (=1.2 atm), and P* (= 483.3 mmHg, calculated from Antoines equation, a,b, and c given above, and T = 55C), so we can calculate yH1 = .5299, and thus yM1 = .4701. And it follows that,

Totaln-HexaneMethane
F119.7510.469.287
F29.992.70449.287
F3
X


furthermore,

Totaln-HexaneMethane
F119.7510.469.287
F29.992.70449.287
F39.759.75
X




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